Every year on and around september 11th my friend asks me what happened on november 9th. I say I don't know.

Same thing happens here. Although, apparently a true story: one European company was doing transatlantic business and was being supplied by an American firm. Items kept arriving late or occasionally, very early. Eventually they worked it out - one was using, for example, 5/7/02 and the other was using 7/5/02; both meaning the same but apparently viewing the other's dates in their own format. They must have been embarrassed at the end.

Personally I've never understood it - I mean, day -> month -> year is logical, an ascending progression of time from the smallest iteration to the greatest. Just like hour -> minute -> second. You would never write the time hh:ss:mm, would you? NO LOGIC!

mm/dd/yy is written as it would be spoken in abbreviated form:
November 27th, 2006

dd/mm/yy doesn't roll off the tongue quite as smoothly:
The 27th of November, 2006

Ha! Nature versus nurture. dd/mm/yy rolls off my tongue very smoothly indeed and I have trouble with the American way, particularly when the ordinal is left out ("November 27, 2006"). It only seems awkward for you because you've grown up used to something different. Either method is only a matter of practice and getting used to it; however, the British (or at least non-US) method is more logical, and that's the single point in favour of one or the other.